1. Field of the Invention
The present invention relates to signal demodulation technology, and, more particularly, to a demodulation apparatus and method using a code table in a soft demodulator, which decreases complexity and increases demodulation efficiency.
2. Description of the Related Art
Generally, in an environment utilizing high-density optical recording media, inter symbol interference (ISI) exists, and data is modulated using run-length limited (RLL) codes.
When conventional RLL codes are decoded, a channel demodulator, for example, a Viterbi decoder, detects code words from a signal input through a channel, and an RLL decoder decodes the code words into data words using a decoding table.
Recently, soft demodulators and soft decoders have experienced increased usage. The above-described Viterbi decoder directly outputs a code word, which contains an error and has only a value of 1 or −1. This method is referred to as hard demodulation. However, in soft demodulation, a soft channel detector receives a channel signal and outputs the probability value of a code word. In other words, the soft channel detector outputs an analog value such as 0.8 or −0.8 containing the probability of a code value being 1 or −1. A soft demodulator receives data indicating the probability value of the code word and outputs the probability value of a data word. Then, a soft decoder, such as a turbo decoder, receives and decodes the probability value of the data word, and forms the data word.
Turbo decoding requiring soft modulation was introduced by Laura L. McPheters and Steven W. McLaughlin [“Turbo-Coded Optical Recording Channels with DVD Minimum Mark Size”, IEEE Transactions on Magnetics, Vol. 38, No. 1, pp. 298–302, January].
The following description concerns the operation of the above-described soft demodulator, which receives data indicating the probability value of a code word and obtains a log likelihood ratio (LLR) value indicating the probability of each bit constituting a data word. The operation will be described with reference to the table shown in FIG. 1.
FIG. 1 shows a decoding table having a code rate of 2/3 for RLL(1, 7) codes. The first row of the table shows 2-bit data words resulting from the decoding process, and the values shown below each of the data words are the code words corresponding to each data word. FIG. 1 shows an example of using a 9-bit code word in order to decode a 2-bit data word.
In order to obtain an LLR value, A Posteriori Probability (APP) (dk=1) and APP(dk=0) are calculated. APP(dk=1) is a value indicating the probability of demodulated data dk being 1, and APP(dk=0) is a value indicating the probability of demodulated data dk being 0. When the length of a code word, which is used for determining a data word, is t bits, values of rm−(2*cm−1))2 are obtained for the individual bits of a code word setting one bit of the data word to 1, and then the values are summed up. Here, m=0, . . . , t-1. APP(dk=1) is obtained by summing up the exponential values obtained with respect to all M code words, which set one bit of the data word to 1, as shown in Formula (1).
                              APP          ⁡                      (                                          d                k                            =              1                        )                          =                              ∑                          j              ∈                                                S                  1                                ⁡                                  (                  k                  )                                                              ⁢                      exp            ⁡                          [                                                (                                                            r                      m                      j                                        -                                          (                                                                        2                          *                                                      c                            m                            j                                                                          -                        1                                            )                                                        )                                2                            ]                                                          (        1        )            
Here, j indicates that a value of a j-th data word is 1, and S1(k) is the set of entries corresponding to dkdk+1=10 and entries corresponding to dkdk+1=11 in the table shown in FIG. 1.
APP(dk=0) is obtained in the same manner as APP(dk=1), that is, it is obtained according to Formula (2).
                              APP          ⁡                      (                                          d                k                            =              0                        )                          =                              ∑                          j              ∈                                                S                  0                                ⁡                                  (                  k                  )                                                              ⁢                      exp            ⁡                          [                                                (                                                            r                      m                      j                                        -                                          (                                                                        2                          *                                                      c                            m                            j                                                                          -                        1                                            )                                                        )                                2                            ]                                                          (        2        )            
Here, S0(k) is the set of entries corresponding to dkdk+1=00 and entries corresponding to dkdk+1=01 in the table shown in FIG. 1.
LLR(dk) is the exponential value of a ratio expressed by Formula (3). The ratio is defined as the probability that one bit of the data word dk resulting from demodulation of a received code word is 0 to the probability that the one bit of the data word dk is 1. LLR(dk) is an output of the soft demodulator.
                                                                                          LLR                  ⁡                                      (                                          d                      k                                        )                                                  =                                ⁢                                  log                  ⁡                                      (                                                                  Pr                        ⁡                                                  (                                                                                    d                              k                                                        =                                                          1                              ❘                              R                                                                                )                                                                                            Pr                        ⁡                                                  (                                                                                    d                              k                                                        =                                                          0                              ❘                              R                                                                                )                                                                                      )                                                              ,                              R                =                                  r                  0                                            ,                              r                1                            ,              …              ⁢                                                          ,                              r                                  t                  -                  1                                                                                                        =                            ⁢                              log                ⁡                                  (                                                            Pr                      ⁡                                              (                                                                              R                            ❘                                                          d                              k                                                                                =                          1                                                )                                                                                    Pr                      ⁡                                              (                                                                              R                            ❘                                                          d                              k                                                                                =                          0                                                )                                                                              )                                                                                                                      ⁢                              (                                  log                  ⁡                                      (                                                                                            ∑                                                      j                            ∈                                                                                          S                                1                                                            ⁡                                                              (                                k                                )                                                                                                                                    ⁢                                                  Pr                          ⁡                                                      (                                                          R                              ❘                                                                                                C                                  j                                                                ⁢                                transmitted                                                                                      )                                                                                                                                                ∑                                                      j                            ∈                                                                                          S                                0                                                            ⁡                                                              (                                k                                )                                                                                                                                    ⁢                                                  Pr                          ⁡                                                      (                                                          R                              ❘                                                                                                C                                  j                                                                ⁢                                transmitted                                                                                      )                                                                                                                )                                                  )                                                                        (        3        )            
When the assumption is made that the frequency of Cj in S0(k) is the same as that in S1(k), the probability Pr(R|Cj) is expressed by Formula (4).
                              Pr          ⁡                      (                          R              ❘                              C                j                                      )                          =                                            (                              1                                                                            2                      ⁢                      π                                                        ⁢                  σ                                            )                        t                    ⁢                      exp            ⁡                          [                                                -                                      1                                          2                      ⁢                                              σ                        2                                                                                            ⁢                                                      ∑                                          m                      =                      0                                                              t                      -                      1                                                        ⁢                                                            (                                                                        r                          m                          j                                                -                                                  (                                                                                    2                              *                                                              c                                m                                j                                                                                      -                            1                                                    )                                                                    )                                        2                                                              ]                                                          (        4        )            
Accordingly, Formula (3) can be rewritten as Formula (5).
                                                                        log                ⁡                                  (                                                                                    ∑                                                  j                          ∈                                                                                    S                              1                                                        ⁡                                                          (                              k                              )                                                                                                                          ⁢                                              Pr                        ⁡                                                  (                                                      R                            ❘                                                                                          C                                j                                                            ⁢                              transmitted                                                                                )                                                                                                                                    ∑                                                  j                          ∈                                                                                    S                              0                                                        ⁡                                                          (                              k                              )                                                                                                                          ⁢                                              Pr                        ⁡                                                  (                                                      R                            ❘                                                                                          C                                j                                                            ⁢                              transmitted                                                                                )                                                                                                      )                                            =                            ⁢                              log                ⁢                                                                            ∑                                              j                        ∈                                                                              S                            1                                                    ⁡                                                      (                            k                            )                                                                                                                ⁢                                          exp                      ⁡                                              [                                                                              1                                                          σ                              2                                                                                ⁢                                                                                    ∑                                                              m                                =                                0                                                                                            t                                -                                1                                                                                      ⁢                                                                                          r                                m                                j                                                            *                                                              (                                                                                                      2                                    *                                                                          c                                      m                                      j                                                                                                        -                                  1                                                                )                                                                                                                                    ]                                                                                                                        ∑                                              j                        ∈                                                                              S                            0                                                    ⁡                                                      (                            k                            )                                                                                                                ⁢                                          exp                      ⁡                                              [                                                                              1                                                          σ                              2                                                                                ⁢                                                                                    ∑                                                              m                                =                                0                                                                                            t                                -                                1                                                                                      ⁢                                                                                          r                                m                                j                                                            *                                                              (                                                                                                      2                                    *                                                                          c                                      m                                      j                                                                                                        -                                  1                                                                )                                                                                                                                    ]                                                                                                                                                                    =                            ⁢                                                log                  ⁢                                                            ∑                                              j                        ∈                                                                              S                            1                                                    ⁡                                                      (                            k                            )                                                                                                                ⁢                                          exp                      ⁡                                              [                                                                              1                                                          σ                              2                                                                                ⁢                                                                                    ∑                                                              m                                =                                0                                                                                            t                                -                                1                                                                                      ⁢                                                                                          r                                m                                j                                                            *                                                              (                                                                                                      2                                    *                                                                          c                                      m                                      j                                                                                                        -                                  1                                                                )                                                                                                                                    ]                                                                                            -                                                                                                      ⁢                              log                ⁢                                                      ∑                                          j                      ∈                                                                        S                          0                                                ⁡                                                  (                          k                          )                                                                                                      ⁢                                      exp                    ⁡                                          [                                                                        1                                                      σ                            2                                                                          ⁢                                                                              ∑                                                          m                              =                              0                                                                                      t                              -                              1                                                                                ⁢                                                                                    r                              m                              j                                                        *                                                          (                                                                                                2                                  *                                                                      c                                    m                                    j                                                                                                  -                                1                                                            )                                                                                                                          ]                                                                                                                                                            ⁢                                                                    (                                    ⁢                                                            max                                              j                        ∈                                                                              S                            1                                                    ⁡                                                      (                            k                            )                                                                                                                ⁢                                          [                                                                        1                                                      σ                            2                                                                          ⁢                                                                              ∑                                                          m                              =                              0                                                                                      t                              -                              1                                                                                ⁢                                                                                    r                              m                              j                                                        *                                                          (                                                                                                2                                  *                                                                      c                                    m                                    j                                                                                                  -                                1                                                            )                                                                                                                          ]                                                                      -                                                                                                      ⁢                                                max                                      j                    ∈                                                                  S                        0                                            ⁡                                              (                        k                        )                                                                                            ⁢                                  [                                                            1                                              σ                        2                                                              ⁢                                                                  ∑                                                  m                          =                          0                                                                          t                          -                          1                                                                    ⁢                                                                        r                          m                          j                                                *                                                  (                                                                                    2                              *                                                              c                                m                                j                                                                                      -                            1                                                    )                                                                                                      ]                                                                                        (        5        )            
When max-log approximation is used as expressed by Formula (6), Formula (5) can be rewritten as Formula (7) because the same performance is exhibited even if
  1      σ    2  is ignored.log(eδ1+eδ2+. . . +eδn)(maxj∈{1,2, . . . , n}δj)  (6)
In other words, the LLR(dk) is obtained, as shown in Formula (7), by calculating a maximum value instead of an exponential value, when exponential calculation is complex, and calculating APP(dk=1)−APP(dk=0), instead of performing the division expressed in Formula (3).
                              LLR          ⁡                      (                          d              k                        )                          =                                            max                              j                ∈                                                      S                    1                                    ⁡                                      (                    k                    )                                                                        ⁢                          [                                                ∑                                      m                    =                    0                                                        t                    -                    1                                                  ⁢                                                      r                    m                    j                                    *                  2                  ⁢                                      (                                                                  c                        m                        j                                            -                      1                                        )                                                              ]                                -                                    max                              j                ∈                                                      S                    0                                    ⁡                                      (                    k                    )                                                                        ⁢                          [                                                ∑                                      m                    =                    0                                                        t                    -                    1                                                  ⁢                                                      r                    m                    j                                    *                  2                  ⁢                                      (                                                                  c                        m                        j                                            -                      1                                        )                                                              ]                                                          (        7        )            
LLR(dk+1) can be obtained by applying k+1, instead of k, to Formula (7), as shown in Formula (8).
                              LLR          ⁡                      (                          d                              k                +                1                                      )                          =                                            max                              j                ∈                                                      S                    1                                    ⁡                                      (                                          k                      +                      1                                        )                                                                        ⁢                          [                                                ∑                                      m                    =                    0                                                        t                    -                    1                                                  ⁢                                                      r                    m                    j                                    *                  2                  ⁢                                      (                                                                  c                        m                        j                                            -                      1                                        )                                                              ]                                -                                    max                              j                ∈                                                      S                    0                                    ⁡                                      (                                          k                      +                      1                                        )                                                                        ⁢                          [                                                ∑                                      m                    =                    0                                                        t                    -                    1                                                  ⁢                                                      r                    m                    j                                    *                  2                  ⁢                                      (                                                                  c                        m                        j                                            -                      1                                        )                                                              ]                                                          (        8        )            
Here, S0(k+1) is the set of entries corresponding to dkdk+1=00 and entries corresponding to dkdk+1=10 in the table shown in FIG. 1, and S1(k+1) is the set of entries corresponding to dkdk+1=01 and entries corresponding to dkdk+1=11 in the table shown in FIG. 1.
As described above, when the size of an APP decoding table used in the conventional soft demodulator increases, the time required for calculating an LLR also increases, and the APP decoding table becomes remarkably complicated.